Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

Abstract

The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the shear rate and the trap distance. Shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are linear in the shear rate, asymmetric in time, and occur for one particle as well as between both particles. Moreover, the shear rate enters as a quadratic correction to the well-known correlations of random displacements along parallel spatial directions. The correlation functions depend on the orientation of the connection vector between the potential minima with respect to the flow direction. As a consequence, the inter-particle cross-correlations between orthogonal fluctuations can have zero, one or two local extrema as a function of time. Possible experiments for detecting these predicted correlations are described.

Brownian dynamics without Green's functions

“…Particles are anchored with a harmonic spring to their initial locations and subjected to shear flow, as can be experimentally realized by using optical tweezers to apply the potential [84]. Brammert, Holzer, and Zimmerman have performed theoretical analysis of this system [85,86] and provide explicit expressions used to test the accuracy of our scheme. The numerical results presented below demonstrate the ability of our midpoint schemes to correctly reproduce the effect of hydrodynamic interactions between distinct immersed particles.…”

Hydrodynamic interactions of colloidal spheres under shear flow

“…We briefly review the work of Zimmermann and co-workers [2,3]: The systems condsidered here are that of one and of two hard spherical particles trapped in harmonic potential wells and suspended in a shear flow with a linear velocity profile. Here and in the following the Brownian spheres have the same mass M i = M and the same effective radii ̺ i = ̺ with i = 1, 2.…”

“…Recently Zimmermann and co-workers presented a series of articles on the correlations that are induced between two trapped colloidal particles by shear flow. They addressed the problem experimentally [1] and theoretically [2,3]. The experimental system consisted of uncharged polystyrene beads suspended in water in a microfluidic device that allowed to create a linear shear profile.…”

Stochastic interactions of two Brownian hard spheres in the presence of depletants

“…The cross-correlation analysis of hydrodynamic interactions of two particles was studied experimentally using optical tweezers [31][32][33]. The method has been extended to investigate the dynamics of optically bounded particles [34] and the shear effect [35,36].…”